For infinite networks, \(\mathsf {LCN}_\infty = \mathsf {VEC}_\infty \)  [1]}, [2]}, [3]}. The kernels
of \(\mathsf {VEC}_\infty \)  and \(\mathsf {GAP}_\infty \)  are of the forms
\(\Theta _{\mathsf {VEC}}(x, x^{\prime }) &= k(\lbrace \langle x_\alpha , x^{\prime }_\alpha \rangle \rbrace _{\alpha \in [d]})\\\Theta _{\mathsf {GAP}}(x, x^{\prime }) &= k(\lbrace \langle x_\alpha , x^{\prime }_{\alpha ^{\prime }}\rangle \rbrace _{\alpha , \alpha ^{\prime }\in [d]}).\) 
